A Joint Learning and Optimization Approach for the Two-Stage Stochastic Service Network Design Problem

Abstract Freight consolidation carriers must plan shipping capacity for an upcoming operating season under uncertainty in shipment volumes. This often takes the form of an optimization problem: a two-stage Stochastic Service Network Design (SSND) problem, that is computationally intractable for realistic network sizes. We propose a neural network-augmented optimization framework for such a problem with general integer first-stage variables. The approach replaces the computationally expensive second-stage recourse cost subproblem with a feedforward neural network embedded directly into a mixed-integer programming formulation, which is solved as a surrogate model. Unlike prior work adopting such an approach, which assumes (bounded) binary first-stage, a challenge for effective learning in this setting is generating training data that adequately covers a bigger feasible solution space. Thus, we introduce and compare three data generation strategies: a random approach, a novel perturbation-based approach that seeds training samples from solutions of single-scenario problems, and a hybrid of the two. Experiments across 18 instances show that the choice of data generation method impacts solution quality and that the approach, overall, is a viable heuristic for this class of problems. The perturbation-based and hybrid approaches both outperform the random approach on a variety of metrics, and they result in better service network designs. The perturbation and hybrid approaches are then further benchmarked against Sample Average Approximation (which is often used to solve this problem) and results show comparable solution quality while offering complementary trade-offs in computational effort and scalability, thus making the framework a viable alternative for freight consolidation carriers.